1.

The solution set of the equation `"log"_(x)2 xx "log"_(2x)2 = "log"_(4x) 2,` isA. `{2^(-sqrt(2)), 2^(sqrt(2))}`B. `{(1)/(2), 2}`C. `{(1)/(4), 4}`D. none of these

Answer» Correct Answer - A
We have,
`"log"_(x) 2 xx "log"_(2x) 2 = "log"_(4x)2`
`rArr (1)/("log"_(2)x) xx (1)/("log"_(2)2x) = (1)/("log"_(2)4x), x ne 1, x gt 0`
`rArr (1)/("log"_(2)x) xx (1)/((1+"log"_(2)x)) = (1)/((2+"log"_(2)x))`
`rArr ("log"_(2)x + 2) = ("log"_(2)x)(1+"log"_(2)x)`
`rArr ("log"_(2)x)^(2) = 2 rArr "log"_(2) x = +- sqrt(2) rArr x = 2^(sqrt(2)), 2^(-sqrt(2))`


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